It’s 50°F and sunny in Wisconsin, according to the local forecast. The cold days are almost done, and so too is the Republican primary. In the week leading up to Tuesday’s nominating contest in the state, one of the few standing between Mitt Romney and ironclad inevitability, GOP leaders rallied to the former governor’s banners. National figures like Jeb Bush and Marco Rubio signed on to the campaign, as did home-state heroes like Senator Ron Johnson and Representative Paul Ryan. Romney finally has the party at his back. But that support also puts a new kind of burden on his shoulders.

A hard-fought primary season has done Romney and his party few favors. According to a March survey conducted by the Pew Research Center for the People and the Press, 56% of Americans hold a negative view of the Republican Party, compared with a 49% plurality who view Democrats favorably. Half of Americans say the GOP is the more extreme party, 15 points more than those who say the same of the Dems.

Despite President Obama’s stewardship of a tepid recovery, rising gas prices and the passage of the controversial health-reform law that is currently before the Supreme Court, more trust his party on the economy, energy and health care than they do the Republicans. The GOP’s signature issue in 2010 and 2011 — sounding the alarm on swelling deficits — is now a wash. Independents are evenly split on most of these issues but still rate Republicans as more extreme.

This kind of data helps explain why Romney is underwater with a 51% unfavorable rating and why uniting the party is a fraught exercise for him. As Romney secures the various factions of the GOP, he risks taking on its baggage too. And a spate of issues, national and local, threaten to distract from Romney’s general-election message that Obama has mishandled the economy and therefore needs to go.

Nowhere is this more apparent than in Wisconsin, which for the past year has been the main front in the war between Republican lawmakers and labor unions. Swept into power in 2010, the GOP, led by Governor Scott Walker, enacted a deep-cutting budget that trimmed benefits and limited the bargaining capability of public workers. The measures sparked a massive backlash from Democrats and their union allies, who put in motion only the third recall vote of a governor in U.S. history.

Walker has not endorsed Romney or any other candidate in Tuesday’s primary, perhaps to avoid alienating the Republican voters he desperately needs in his upcoming recall election. But when he faces the judgment of Wisconsinites on June 5, the general election will just be picking up. Romney, who has long supported Walker and his budget, will be dragged into the fight as his party’s nominee.

Romney has attacked the United Auto Workers to defend his opposition to the 2009 Detroit bailout and has used labor issues to try to drive a wedge between conservatives and Rick Santorum, who played to Pennsylvania unions during his time in the Senate. But labor issues are probably something he’d rather leave behind for the general election. While Wisconsin might be divided, the national electorate is not. Collective-bargaining restrictions similar to those passed in Wisconsin were rolled back by a referendum last year in the key swing state of Ohio. And while many Americans harbor little love for labor unions, they oppose restricting the bargaining rights of public employees by a margin of roughly 2 to 1, according to a seriesof nationalpolls conducted in the spring of 2011. Even then, most support lies in the Deep South, where Romney can count on conservative electorates to vote against Obama.

All that said, Walker probably isn’t the Wisconsinite who will have the most profound effect on the Republican ticket this year; that distinction goes to Ryan, the House Budget Committee chairman and architect of the deep-cutting, entitlement-restructuring fiscal plans passed by the lower chamber for two years running, who endorsed Romney last week.

Throughout these budgets, Ryan has enshrined in legislation, if not law, Republicans’ wishes to see government scaled back, taxes lowered, Medicaid sent to the states and Medicare voucherized. His plans have made the 42-year-old Congressman an object of reverence and adoration on the right. But they have also opened up the party and its nominee to Democratic attacks on scaling back entitlement programs, which remains unpopular among Democrats, independents and even most Republicans. Obama’s political advisers already refer to this as the “Romney-Ryan plan” and are cutting video lumping the two men together.

In May of last year, Romney praised Ryan’s budget without promising to make it part of his campaign platform. “I’m going to have my own plan,” he said. But the past six months have made that distance difficult to maintain. In order to deep-six Newt Gingrich’s candidacy, Romney criticized the former Speaker for briefly bad-mouthing Ryan’s plan, driving Romney closer. When Romney unveiled his Medicare plan early this year, it borrowed heavily from Ryan’s road map, raising the eligibility age for Medicare and offering coverage through vouchers for use in the private market, albeit with traditional Medicare still available. Ryan’s new plan, constructed with the input of Democrat Ron Wyden and recently passed by the House, closely resembled Romney’s, retaining traditional Medicare as an option.

Whatever the GOP offers up as part of its official platform in the fall, there’s no question that it will be judged, both by Republicans and Democrats, with the Ryan plan as a baseline. And it’s possible that Ryan could be on the ticket too. “If that bridge ever came,” he said last week of the vice-presidential slot, “I’d consider it. In the meantime, I’m not dwelling on it.”

Another Republican vice-presidential prospect, Virginia’s popular and ambitious governor, Bob McDonnell, also illustrates the challenges for Romney in picking up the party’s mantle. McDonnell’s strong approval ratings took a hit this year after the legislature debated and passed a controversial law requiring women to receive an ultrasound and hear a description of their fetus before getting an abortion. The original version, which mandated an invasive vaginal ultrasound, was revised to strike that section of the law, but only after a national uproar over the measure pushed McDonnell to change course and request a revision. Nonetheless, a Quinnipiac University poll conducted in March found that the governor’s approval rating among women dropped 15 points in just one month.

Virginia is a vital state for Romney, but his challenge lies beyond the Old Dominion as well. Republican lawmakers in 20 states have passed mandatory ultrasound laws, and five more besides Virginia debated them this year. Americans have historically been split on whether abortion should be legal, but laws seeking to discourage women from seeking the service are not viewed the same way. Although a slim 52% majority opposed Virginia’s ultrasound law in the Quinnipiac poll, 72% said the government should not try to persuade women not to have an abortion. In the national Pew survey, Democrats’ largest lead on any single issue was the 16-point margin for which party “best represents your views on abortion.”

Romney’s record on the issue is mild — after all, he ran for governor of Massachusetts as a personally antiabortion but professionally pro-abortion-rights candidate before becoming a pro-life presidential prospect — but Republican legislatures in states like Virginia could do residual damage to him among women, especially single women, a group that is emerging as a crucial swing vote, as the candidate and party merge into one. After a winter that saw national debate over mandatory ultrasounds, birth control coverage and Planned Parenthood funding, a USA Today/Gallup poll released on Monday of a dozen battleground states found Obama opening up big leads as women shifted to his side.

Whether these issues plague Romney or not, the Republicans’ best shot at the White House ultimately lies in making the election about Obama and his record in office: a referendum rather than a binary choice. And that’s what Romney was working hard at over the weekend in Wisconsin. “President Obama believes in a government-centered society. He believes government guiding our lives will do a better job in doing so than individuals,” he said on Saturday in Waukesha County. But outside another Romney event on the same day, protesters lined up with signs that read “Recall Walker” and “Keep Your Mitt(s) Off Birth Control.”